If ₀^1 f(x) d x=1, ₀^1 x f(x) d x=a and ₀^1 x^2 f(x) d x=a^2 , then ₀^1(x-a)^2 f(x) d x is equal to

Step-by-step solution

aligned & ₀^1(x-a)^2 f(x)= ₀^1 (x^2 f(x)+a^2 f(x)-2 a x f(x) ) d x & = ₀^1 x^2 f(x) d x+a^2 ₀^1 f(x) d x-2 a ₀^1 x f(x) d x & =a^2+a^2(1)-2 a(a) & =a^2+a^2-2 a^2=0 aligned